Mathematical study of a staged-progression HIV model with imperfect vaccine

Abba Gumel, Connell C. McCluskey, P. Van Den Driessche

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

A staged-progression HIV model is formulated and used to investigate the potential impact of an imperfect vaccine. The vaccine is assumed to have several desirable characteristics such as protecting against infection, causing bypass of the primary infection stage, and offering a disease-altering therapeutic effect (so that the vaccine induces reversal from the full blown AIDS stage to the asymptomatic stage). The model, which incorporates HIV transmission by individuals in the AIDS stage, is rigorously analyzed to gain insight into its qualitative features. Using a comparison theorem, the model with mass action incidence is shown to have a globally-asymptotically stable disease-free equilibrium whenever a certain threshold, known as the vaccination reproduction number, is less than unity. Furthermore, the model with mass action incidence has a unique endemic equilibrium whenever this threshold exceeds unity. Using the Li-Muldowney techniques for a reduced version of the mass action model, this endemic equilibrium is shown to be globally-asymptotically stable, under certain parameter restrictions. The epidemiological implications of these results are that an imperfect vaccine can eliminate HIV in a given community if it can reduce the reproduction number to a value less than unity, but the disease will persist otherwise. Furthermore, a future HIV vaccine that induces the bypass of primary infection amongst vaccinated individuals (who become infected) would decrease HIV prevalence, whereas a vaccine with therapeutic effect could have a positive or negative effect at the community level.

Original languageEnglish (US)
Pages (from-to)2105-2128
Number of pages24
JournalBulletin of Mathematical Biology
Volume68
Issue number8
DOIs
StatePublished - Nov 2006
Externally publishedYes

Fingerprint

Vaccines
Vaccine
vaccine
human immunodeficiency virus
Progression
Imperfect
HIV
vaccines
Infection
Reproduction number
Therapeutic Uses
Endemic Equilibrium
Globally Asymptotically Stable
acquired immune deficiency syndrome
bypass
Reproduction
Acquired Immunodeficiency Syndrome
Incidence
AIDS Vaccines
Model

Keywords

  • Global stability
  • HIV/AIDS
  • Staged progression
  • Vaccination reproduction number

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this

Mathematical study of a staged-progression HIV model with imperfect vaccine. / Gumel, Abba; McCluskey, Connell C.; Van Den Driessche, P.

In: Bulletin of Mathematical Biology, Vol. 68, No. 8, 11.2006, p. 2105-2128.

Research output: Contribution to journalArticle

Gumel, Abba ; McCluskey, Connell C. ; Van Den Driessche, P. / Mathematical study of a staged-progression HIV model with imperfect vaccine. In: Bulletin of Mathematical Biology. 2006 ; Vol. 68, No. 8. pp. 2105-2128.
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